A large hospital wholesaler, as part of an assessment of workplace safety, gave

Question

A large hospital wholesaler, as part of an assessment of workplace safety, gave a random sample of 64 of its warehouse employees a test (measured on a 0 to 100 point scale) on safety procedures. For that sample of employees, the mean test score was 75 points, with a standard deviation of 15 points. We will walk through several question to help us determine and interpret a 90% confidence interval for the mean test score of all the company’s warehouse employees. Determine and interpret a 90% confidence interval for the mean test score of all the company’s warehouse employees. (Please keep at least four decimal places). Carry your math out to FOUR significant decimal places - BUT ROUND YOUR FINAL ANSWER TO TWO What is the LOWER BOUND of the 90% confidence interval (for example, if the interval was 65 to 85, 65 would be the lower bound).

Explanation / Answer

Sol:

n=64

xbar=75

sd=s=15

alpah1-0.9=0.1

alpha/2=0.1/2=0.05

df=n-1=64-1=63

t crit=1.6694

90% confidence interval for the mean test score of all the company’s warehouse employees

=xbar-ts/sqrt(n),xbar+t*s/sqrt(n)

=75-1.6694*15/sqrt(64),75+1.6694*15/sqrt(64)

=71.87,78.13

we are 90% confidence interval that the mean test score of all the company’s warehouse employees

lies in between 71.87 and 78.13

lower imiit=71.87

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